A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found that for a shrinking mass scale due to evaporation, the null radial geodesics that generate the horizon are (...) slightly displaced from the coordinate singularity. In addition, a changing horizon scale significantly alters the form of the coordinate singularity in diagonal (orthogonal) metric coordinates representing the space-time. A Penrose diagram describing the growth and evaporation of an example black hole is constructed to examine the evolution of the coordinate singularity. (shrink)
The positions Ross & Spurrett (R&S) take on issues of information, causality, functionalism, and emergence are actually implicit in the theory and practice of statistical physics, specifically in the way it relates macroscopic collective coordinates to microscopic physics. The reasons for taking macroscopic physical variables like temperature or magnetization to be real apply equally to mental properties like pain.
The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in (...) quantum mechanics are unbounded. Often one finds statements such as: For any linear operator A we can write a Hermitian operator HA=(A+A+)/2, where Hermitian is thought to mean self-adjoint. Along these lines, self-adjointness of the momentum operator in generalized coordinates, taken from that expression, is questioned. In particular, the redescription in terms of spherical polar coordinates and its implications for the eventual loss of self-adjointness of the momenta conjugate to them are studied. (shrink)
Traditional lore holds that there is only one way to represent local symmetry, leading to practically unique gauge theories. However there is more than one path to local symmetry. Here I discuss expressing the theory of dressed quarks, gluons and other particles using new variables. The gauge sector is expressed with fields ea μ which transform homogeneously like matter fields under the gauge group. Consistency requires further embedding in a larger global group. Many interesting topics of gauge theories, from the (...) elementary nature of the Coulomb field to magnetic monopoles, serve as illustrations. Geometrical invariants forbidden in the standard coordinates become available in the new approach. I argue that these are natural, and useful, in the description of an effective theory. For example, in a covariant derivative expansion, one can express a massively propagating gauge invariant effective theory in four space-time dimensions. (shrink)
The classical Hamiltonian in generalized coordinates is given asH=1/2 Σ i.k p i g ik p k . We show that there is no operator of the formP i= −iA(qi) (∂/∂qi)+Gi(qi) (note that the Hermitian momentum operatorP i H is of this form) such that the quantum Hamiltonian operatorH Q is given asH Q =1/2 Σ i,k P i g ik P k or1/2 Σ i,k g ik P i P k , etc. In order to maintain a direct (...) transition of this sort from classical to quantum theory, using the classical Hamiltonian as a starting point, we must rely on our previous prescriptions, writing the quantum Hamiltonian asH Q =1/2 Σ i,k P i + g ik P k , whereP i + denotes the adjoint of the operatorP i=−ih ∂/∂qi. (shrink)
Recent advanced statistical analysis of complex spikes has revealed that their instantaneous firing rate within a time bin of a few milliseconds carries information if many trials are averaged, as happens in motor learning. The firing rate encodes sensory error signals in the inverse-dynamics motor-command coordinates, and these are exactly the same coordinates as for simple spikes. This strongly supports the most critical assumption of the feedback-error-learning model and argues against several hypotheses about the functions of the complex (...) spikes. [HOUK et al.; SIMPSON et al.; SMITH; THACH]. (shrink)
The law of gravitation is taken in the formR 44=0, whereR 44 is the time curvature component of the Ricci tensor. Space-time separable equations are developed in spherical coordinates for the nonlinear wave equation determined byR 44=0. One exact solution is examined in detail.
The quantum harmonic oscillator is described in terms of two basic sets of coordinates: linear coordinates x, px and angular coordinates eiφ, Pφ (action-angle variables). The angular “coordinate” eiφ is assumed unitary, the conjugate momentum pφ is assumed Hermitian, and eiφ and pφ are assumed to be a canonical pair. Two transformations are defined connecting the angular coordinates to the linear coordinates. It is found that x, px can be physical, i.e., Hermitian and canonical, only (...) under constraints on the pφ eigenvalue spectrum. The conclusion is that eiφ can be a unitary operator. A parallel analysis of the classical harmonic oscillator is done with equivalent results. (shrink)
The experimental (apparent) space-time transformations connect coordinates altered by length contraction and clock retardation. When clocks are synchronized by means of light signals (Einstein–Poincaré procedure) or by slow clock transport, the experimental space-time. transformations assume the mathematical form of the “Extended space-time transformations”.(4) These reduce to the Lorentz–Poincaré transformations when one of the frames they connect is the fundamental inertial frame. If the synchronization procedure were perfect, the experimental space-time transformations would assume the form of Selleri’s inertial transformations.(5) The (...) real space-time transformations are those which are disclosed when the systematic measurement distortions are corrected. (shrink)
The brief coda devoted to the Trinity in Schleiermacher's The Christian Faith does not intend to marginalize the doctrine. It indicates that the doctrine, though at present still to be completed, is the recapitulation of the entire scheme of redemption. The central structuring concept in that scheme is that of the genuine union between the divine existence of the infinite creator and human nature in Christ, a pattern replicated in the coming of the Holy Spirit as the inauguration of a (...) second, strictly analogous union of God and humanity. The subtle way in which Schleiermacher conceives these unions in line with his rigorous understanding of radical causality of divine creation requires careful unpacking. Only such an analysis brings to light the architecture of the doctrine of the Trinity, and its function as a kind of meta-doctrine, connecting and coordinating different elements in the doctrine of grace. (shrink)
Since the very begining of quantum theory there started a debate on the proper role of space and time in it. Some authors assumed that space and time have their own algebraic operators. On that basis they supposed that quantum particles had “coordinates of position”, even though those coordinates were not possible to determine with infinite precision. Furthermore, time in quantum physics was taken to be on an equal foot, by means of a so-called “Heisenberg’s fourth relation of (...) indeterminacy” concerning time and energy. In this paper, the proper role of space and time in the core of non-relativistic quantum phsysics is analyzed. We will find that, rigorously, that relation for time and energy shows a different root. For the role of space, it will be discussed that there is no “coordinate of position” in the conceptual structure of quantum physics because quantum particles are not point-like objects. DOI:10.5007/1808-1711.2010v14n2p241. (shrink)
A time dependent “cosmological constant” Λ(t) is conjectured, in terms of the Gaussian curvature of the causal horizon. It is nonvanishing even in Minkowski space because of the lack of informations beyond the light cone. Using the Heisenberg Principle, the corresponding energy of the quantum fluctuations localized on the past or future null horizons is proportional to Λ1/2.We compute Λ(t) for the (Lorenzian version) of the (conformally flat) Hawking wormhole geometry (written in static spherical Rindler coordinates) and for the (...) de Sitter spacetime. A possible explanation of the Hawking temperature is proposed, in terms of a constant Λ. (shrink)
The operator form of the generalized canonical momenta in quantum mechanics is derived by a new, instructive method and the uniqueness of the operator form is proven. If one wishes to find the correct representation of the generalized momentum operator, he finds the Hermitian part of the operator —iħ ∂/∂q, whereq q is the generalized coordinate. There are interesting philosophical implications involved in this: It is like saying that a physical structure is composed of two parts, one which is real (...) (the measurable quantity) and one which is pure imaginary. However, in order to understand the theoretical generation of the physical structure, one must look at the imaginary part as well as the real part since the sum of these two parts gives the simplified physical theory. That is why we can choose the total generalized momentum operator as simply —iħ ∂/∂q, but in order to arrive at the “measurable” momentum operator, we must choose the real (Hermitian) part, the other part being anti-Hermitian (corresponding to pure imaginary eigenvalues). We also discuss the operator form of the generalized Hamiltonian and show that the primary focus in developing fundamental concepts and prescriptions in quantum mechanics should be on the generalized momenta rather than on the Hamiltonian. (shrink)
Where modern formulations of relatively theory use differentiable manifolds to space-time, Einstein simply used open sets of R 4 , following the then current methods of differential geometry. This fact aids resolution of a number of outstanding puzzles concerning Einstein's use of coordinate systems and covariance principles, including the claimed physical significance of covariance principles, their connection to relativity principles, Einstein's apparent confusion of coordinate systems and frames of reference, and his failure to distinguish active and passive transformations, especially in (...) the context of his hole and point-coincidence arguments. (shrink)
In recent years, Reichenbach's 1920 conception of the principles of coordination has attracted increased attention after Michael Friedman's attempt to revive Reichenbach's idea of a "relativized a priori". This paper follows the origin and development of this idea in the framework of Reichenbach's distinction between the axioms of coordination and the axioms of connection. It suggests a further differentiation among the coordinating axioms and accordingly proposes a different account of Reichenbach's "relativized a priori".
We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet's elliptical orbit in the Sun's gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in accordance with the hypotheticodeductive model.
The traditional solution concept for noncooperative game theory is the Nash equilibrium, which contains an implicit assumption that playersâ probability distributions satisfy t probabilistic independence. However, in games with more than two players, relaxing this assumption results in a more general equilibrium concept based on joint beliefs (Vanderschraaf, 1995). This article explores the implications of this joint-beliefs equilibrium concept for two kinds of conflictual coordination games: crisis bargaining and public goods provision. We find that, using updating consistent with Bayesâ rule, (...) playersâ beliefs converge to equilibria in joint beliefs which do not satisfy probabilistic independence. In addition, joint beliefs greatly expand the set of mixed equilibria. On the face of it, allowing for joint beliefs might be expected to increase the prospects for coordination. However, we show that if players use joint beliefs, which may be more likely as the number of players increases, then the prospects for coordination in these games declines vis-Ã -vis independent beliefs. (shrink)
Following Schelling (1960), coordination problems have mainly been considered in a context where agents can achieve a common goal (e.g., rendezvous) only by taking common actions. Dynamic versions of this problem have been studied by Crawford and Haller (1990), Ponssard (1994), and Kramarz (1996). This paper considers an alternative dynamic formulation in which the common goal (dispersion) can only be achieved by agents taking distinct actions. The goal of spatial dispersion has been studied in static models of habitat selection, location (...) or congestion games, and network analysis. Our results show how this goal can be achieved gradually, by indistinguishable non-communicating agents, in a dynamic setting. (shrink)
This paper investigates the influence that social ties can have on behavior. After defining the concept of social ties that we consider, we introduce an original model of social ties. The impact of such ties on social preferences is studied in a coordination game with outside option. We provide a detailed game theoretical analysis of this game while considering various types of players, i.e., self-interest maximizing, inequity averse, and fair agents. In addition to these approaches that require strategic reasoning in (...) order to reach some equilibrium, we also present an alternative hypothesis that relies on the concept of team reasoning. After having discussed the differences between the latter and our model of social ties, we show how an experiment can be designed so as to discriminate among the models presented in the paper. (shrink)
Many science systems are witnessing the rise of intermediary organizations with a coordinating mission, but to date a systematic understanding of their function and effects is lacking. The aim of this paper is to contribute to the understanding of the coordinating efforts of intermediary organizations. Starting from the definition of coordination as the establishment or strengthening of a relationship among the activities in a system, with the aim to enhance their common effectiveness, I develop a heuristic framework that facilitates the (...) systematic analysis of coordination in science. I illustrate and substantiate my framework with the empirical case study of a Dutch coordination task force in the area of chemical technologies. Thanks to the framework I could disentangle a number of functions that this task force fulfils concerning research programming, funding allocation and supporting interactions and collaborations. This approach enabled me to systematically analyse a very heterogeneous set of processes that each deserve to be called coordination. The analysis yields a clear overview of eight coordination processes that are each described in terms of activities, intervention, relationships, mechanisms and performance. I conclude my paper with suggestions for further research on coordination in the science system. (shrink)
We calculate the Lebesgueâmeasures of the stability sets of Nash-equilibria in pure coordination games. The results allow us to observe that the ordering induced by the Lebesgueâmeasure of stability sets upon strict Nash-equilibria does not necessarily agree with the ordering induced by riskâdominance. Accordingly, an equilibrium selection theory based on the Lebesgueâmeasure of stability sets would be necessarily different from one which uses the Nash-property as a point of orientation.
To understand how groups coordinate, we study infinitely repeated N-player coordination games in the context of strategic uncertainty. In a situation where players share no common language or culture, ambiguity is always present. However, finding an adequate principle for a common language is not easy: a tradeoff between simplicity and efficiency has to be made. All these points are illustrated on repeated N-player coordination games on m loci. In particular, we demonstrate how a common principle can accelerate coordination. We present (...) very simple rules that are optimal in the space of all languages for m (number of coordination loci) from 2 to 5 and for all N, the number of players. We also show that when more memory is used in the language (strategies), players may not coordinate, whereas this is never the case when players remember only the previous period. (shrink)
ChickenHawk is a social-dilemma game that distinguishes uncoordinated from coordinated cooperation. In tests with players belonging to a culturally homogeneous population, natural-language “cheap talk” led to efficient coordination, while nonlinguistic signaling yielded uncoordinated altruism. In a subsequent test with players from a moderately more heterogeneous population nearby, the “cheap talk” condition still produced better coordination than other signaling conditions, but at a lower level and with fewer acts of altruism overall. Implications are: (1) without language, even willing cooperators coordinate poorly; (...) (2) given a sufficiently homogeneous social group, language can coordinate cooperation in the face of opportunities for anonymous defection; (3) coordination therefore depends not on merely a general propensity to cooperate but on the overlap of social identities, which are always costly to acquire and maintain. So far as linguistic variation establishes how much social identities overlap, natural-language “cheap talk” is self-insuring, suggesting that linguistic variation is itself adaptive. (shrink)
This paper is concerned with adaptive learning and coordination processes. Implementing agent-based modeling techniques (Learning Classifier Systems, LCS), we focus on the twofold impact of cognitive and environmental complexity on learning and coordination. Within this framework, we introduce the notion of Adaptive Learning Agent with Rule-based Memory (ALARM), which is a particular class of Artificial Adaptive Agent (AAA, Holland and Miller 1991). We show that equilibrium is approached to a high degree, but never perfectly reached. We also demonstrate that memorization (...) and learning capacities depend upon the relative discordance between the cognitive complexity of agents' mental models and the degree of stability of the environment. (shrink)
The coordination of the various processes involved in language production is a subject of keen debate in writing research. Some authors hold that writing processes can be flexibly coordinated according to task demands, whereas others claim that process coordination is entirely inflexible. For instance, orthographic planning has been shown to be resource-dependent during handwriting, but inflexible in typing, even under time pressure. The present study therefore went one step further in studying flexibility in the coordination of orthographic processing and graphomotor (...) execution, by measuring the impact of time pressure during a handwritten copy task. Orthographic and graphomotor processes were observed via syllable processing. Writers copied out two- and three-syllable words three times in a row, with and without time pressure. Latencies and letter measures at syllable boundaries were analyzed. We hypothesized that if coordination is flexible and varies according to task demands, it should be modified by time pressure, affecting both latency before execution and duration of execution. We therefore predicted that the extent of syllable processing before execution would be reduced under time pressure and, as a consequence, syllable effects during execution would be more salient. Results showed, however, that time pressure interacted neither with syllable number nor with syllable structure. Accordingly, syllable processing appears to remain the same regardless of time pressure. The flexibility of process coordination during handwriting is discussed, as is the operationalization of time pressure constraints. (shrink)
Coordination games often have multiple equilibria. The selection of equilibrium raises the question of belief formation: how do players generate beliefs about the behavior of other players? This article takes the view that the answer lies in history, that is, in the outcomes of similar coordination games played in the past, possibly by other players. We analyze a simple model in which a large population plays a game that exhibits strategic complementarities. We assume a dynamic process that faces different populations (...) with such games for randomly selected values of a parameter. We introduce a belief formation process that takes into account the history of similar games played in the past, not necessarily by the same population. We show that when history serves as a coordination device, the limit behavior depends on the way history unfolds, and cannot be determined from a-priori considerations. (shrink)
The Battle of the Sexes game, which captures both coordination and conflict problems, has been applied to a wide range of situations. We show that, by reducing distributional conflict and enhancing coordination, (eventual) turn taking supported by a “turn taking with independent randomizations” strategy allows players to engage in intertemporal sharing of the gain from cooperation. Using this insight, we decompose the benefit from turn taking into conflict-mitigating and coordination-enhancing components. Our analysis suggests that an equilibrium measure of the “degree (...) of intertemporal conflict” provides an intuitive way to understand the sources of welfare gain from turn taking in the repeated Battle of the Sexes game. We find that when this equilibrium measure is lower, players behave less aggressively and the welfare gain from turn taking is higher. (shrink)
This paper reports an experimental investigation of the hypothesis that in coordination games, players draw on shared concepts of salience to identify ‘focal points’ on which they can coordinate. The experiment involves games in which equilibria can be distinguished from one another only in terms of the way strategies are labelled. The games are designed to test a number of specific hypotheses about the determinants of salience. These hypotheses are generally confirmed by the results of the experiment.
When acting jointly with others, adults can be as proficient as when acting individually. However how young children coordinate their actions with another person and how their action coordination develops during early childhood is not well understood. By means of a sequential button-pressing game, which could be played jointly or individually, the action coordination of 2½- and 3-year-old children was examined. Performance accuracy and variability of response timing were taken as indicators of coordination ability. Results showed substantial improvement in joint (...) action coordination between the age of 2½- and 3, but both age groups performed equally well when acting individually. Interestingly, 3-year-olds performed equally well in the joint and the individual condition, whereas 2½-year-olds did not yet show this adult-like pattern as indicated by less accurate performance in the joint action. The findings suggest that in contrast to 3-year-olds, 2½-year-olds still have difficulties in establishing well-coordinated joint action with an adult partner. Possible underlying cognitive abilities such as action planning and action control are discussed. (shrink)
In this paper, I argue on empirical grounds that (VL-initial) Asymmetric Coordination in German cannot be reduced to a syntactic structure of the form [if S1, then S2], but rather needs to be analyzed as some kind of adjunction to the if-clause, i.e., along the lines of [[if S1] and S2]. This conclusion gives rise to an apparent mismatch between syntactic structure (narrow scope of if) and semantic interpretation (wide scope of if). To resolve this paradoxical situation, I propose a (...) compositional semantics for conditionals that is based on the idea that (indexed) if is to be construed as some kind of anaphor (variable) that ranges over objects of type modal base picking up a modal background in the actual context. Even though this analysis assigns a non-vacuous semantics to the complementizer if, it is still compatible with the syntax of Asymmetric Coordination in German, and, in contrast to alternative accounts, avoids the generation of non-existent distributive readings. (shrink)
Coordinating behavior is widespread in contexts that include courtship, aggression, and cooperation for shared outcomes. The social significance of cooperative coordination (CC) is usually downplayed by learning theorists, evolutionary biologists, and game theorists in favor of an individual behavior → outcome perspective predicated on maximizing payoffs for all participants. To more closely model CC as it occurs under free-ranging conditions, pairs of rats were rewarded for coordinated shuttling within a shared chamber with unrestricted social interaction. Results show that animals learned (...) to work together with sensitivity to the task and type of partner. Moreover, social interaction and coordination influenced both consumption of the reward solution immediately following a session and preference for cooperation, suggesting that affective states and incentives related to cooperation extend beyond the outcomes obtained. These results support field studies by showing not only how cooperation is performed but also the importance of considering how the behavior of cooperating affects outcomes and preference for cooperating. (shrink)
We study experimentally a coordination game with N heterogeneous individuals under different information treatments. We explore the effects of information on the emergence of Pareto-efficient outcomes, by means of a gradual decrease of the information content provided to the players in successive experiments. We observe that successful coordination is possible with private information alone, although not on a Pareto-optimal equilibrium. Reinforcement-based learning models reproduce the qualitative trends of the experimental results.
Theoretical and empirical evidence suggests that accurate and efficient motor performance may be achieved by task-specific exploitation of biomechanical degrees of freedom. We investigate coordination of the right arm in a task requiring a sudden yet precisely controlled reversal of movement direction: bow reversals during continuous (“legato”) tone production on a stringed instrument. Ten advanced or professional cello players (at least ten years of practice) and ten age-matched novice players took part in the study. Kinematic data from the bow and (...) the right arm were analyzed in terms of velocity and acceleration profiles, as well as temporal coordination along the arm. As expected, experts’ bow velocity and acceleration profiles differed markedly from those of novice participants, with higher peak accelerations and quicker direction changes. Importantly, experts achieved the change in movement direction with a single acceleration peak while novices tended to use multiple smaller acceleration peaks. Experts moreover showed a proximal-distal gradient in timing and amplitudes of acceleration peaks, with earlier and lower-amplitude reversals at more proximal joints. We suggest that this coordination pattern allows generating high accelerations at the end effector while reducing the required joint torques at the proximal joints. This may underlie experts’ ability to produce fast bow reversals efficiently and with high spatiotemporal accuracy. The findings are discussed in terms of motor control theory as well as potential implications for musicians’ performance and health. (shrink)